Electric Potential Condition¶

The electric potential condition establishes a fixed electric potential \(\phi\) in a given volume or at the boundary of the region of interest:

where \(\Omega\) is the given region of space (volume or surface) and \(\phi_0(x,y,z)\) is the desired distribution of the electric potential.

When to use this¶

• Energised electrodes in a capacitor, MEMS comb-drive, or ion source — apply the terminal voltage.
• Grounded conductors — fix \(\phi_0 = 0\) on the grounded surface.
• Voltage references in HV-insulator and bushing studies.
• Validation benchmarks with prescribed analytic potential profiles.

Usage¶

A scalar value is auto-wrapped into a coefficient:

from mufem.electromagnetics.electrostatics import ElectricPotentialCondition

potential_bc = ElectricPotentialCondition(
    name="Potential = 2 V",
    marker="Electrode::Anode" @ Bnd,
    electric_potential=2.0,
)

electrostatics_model.add_condition(potential_bc)

A coefficient function can be passed directly for space- or time-dependent potentials:

import mufem

cff_potential = mufem.CffExpressionScalar(
    "100.0 * sin(2 * pi * 50 * {Time})"
)

potential_bc = ElectricPotentialCondition(
    name="Driven Electrode",
    marker="Electrode" @ Bnd,
    electric_potential=cff_potential,
)